The non-linear behavior in soft to moderately stiff soils modifies the linear site response, generally by shifting the resonance frequencies towards lower values, and reducing the high-frequency motion in relation to shear modulus decrease and damping increase with increasing loading. The resulting “modulation” of the site response may be quantified by the nonlinear to linear site response ratio, RSRNL-L, comparing the Fourier transfer function for strong events and for weak events. As shown by Régnier et al., this ratio exhibits a “typical shape”; with a low frequency part above 1 and a high frequency part generally below 1, separated by a transition zone around a site-dependent frequency labelled fNL (characterized by RSRNL-L = 1).

The present work intends to compare these observations with the results of extensive non-linear numerical simulation: Non-linear soil behavior results in significant site response modifications even for moderate PGA values of 100 cm/s2, in that case mainly for soft soils with low VS30 value. The resulting RSRNL-L functions exhibit a qualitatively similar shape compared to instrumental data. fNL values exhibit a satisfactory correlation with site classifications based on either VS30 or f0: the lower VS30 or f0, the lower fNL. It is also found that for high-frequency or stiff sites, the ratio fNL/f0 is very close to 1, while it exhibits a large scatter for low frequency sites, with values in the range [1, 10], indicating the concentration of non- linearities in relatively shallow layers. The amount of low-frequency amplification (i.e., for f < fNL) increases with increasing non-linearity, i.e., with increasing PGA and/or strain, and the same for the high-frequency (i.e., f > fNL) reduction.

However, from a quantitative viewpoint, the present numerical simulations seem to overestimate the non-linearity for deep sites with low fundamental frequency. The final aim to propose a model allowing to apply a frequency-dependent “NL modulation” to the measured or computed linear transfer functions, as a function of PGA level and site characteristics, including VS30 and f0, therefore requires further investigations on the actual behavior of such deep deposits.

Corresponding publication: Almakari at el, 2016